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Open AccessArticle

The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function

1
Department of Statistics, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
2
Mobile E-business Collaborative Innovation Center of Hunan Province, Hunan University of Commerce, Changsha 410205, Hunan, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 367; https://doi.org/10.3390/sym10090367
Received: 4 August 2018 / Revised: 18 August 2018 / Accepted: 24 August 2018 / Published: 29 August 2018
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods. View Full-Text
Keywords: hesitant fuzzy linguistic term set; similarity measure; linguistic scale function; distance measure; TOPSIS method hesitant fuzzy linguistic term set; similarity measure; linguistic scale function; distance measure; TOPSIS method
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Liu, D.; Liu, Y.; Chen, X. The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function. Symmetry 2018, 10, 367.

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